No backwards compatibility
Plays used games
Still uses Blu-Ray discs
Suspend/Sleep Mode to quick resume play similar to PSVita/3DS
The "Share" button for livestreaming your personal content
Release date = Holiday 2013
No price...yet

They did not show what the console would look like, but the controller looks to have some really good improvements with the concave analog sticks Like the 360. I have mixed feelings about the backwards compatibility, but I understand why they dropped it. For one, the system would be ridiculously expensive for them to release if they were to have built in PS3 hardware to run the games, and emulating them is just out of the question. So this could potentially make it much cheaper than the PS3 was when it originally launched. Everything else, including the specs are really impressive.

But to answer the backwards compatibility problem, they answered it with their recent purchase of GAIKAI. You'll be able to stream and play PS1-3 games instantly. Not to mention that you can remote play those and PS4 games on the Vita (at least they were just showing the PS4 side).

As for the games themselves. If we really are getting stuff like Deep Down which apparently is all in-game, then color me impressed. I wonder how Microsoft can top this.

Overall I was very impressed. The new hardware specs are great and beyond what I expected, especially the 8GB of GDDR5 memory. Since it's based on x86 tech it almost guarantees that it will be simple to develop for.
It's very smart of them to continue to allow used games. It seems that for this next generation many people will be downloading games anyway so it's less of an issue and won't piss off their early adopters.
The backwards compatibility seems like an overblown issue. I know it's important to some, but in practice this doesn't get used much since people tend to run with the new gen and rarely look back. I expect MS will take a similar approach for their next gen console as well, their backwards compatibility was a hassle on the 360 and didn't end up working well or getting used.
I'm expecting the new MS console will match these hardware specs and both systems will be at the $400 price point for launch. This would be an ideal situation as then MS and Sony can battle it out by offering superior services and games.
sidenote: The Wii U continued to use the Power-PC architecture assuming it would make it easy for 3rd parties to port to the Wii U. Seems they made the wrong choice and are screwed.

Besides the obvious hardware improvements, the one big new feature that I really wanted was integrated livestreaming. Being able to invite online friends to a party and letting them watch you play a game while they comment on what you're doing, a la MST3K, has me very excited. Also, the fact that Sony partnered with Ustream and not Twitch is a good sign that Microsoft gobbled up Twitch for their console. Yay, theater mode for every game.

Hardware be looking good. I still wonder if they've implemented cross-game chat though, maybe I missed it.
I was underwhelmed by their exclusive launch games though minus the new InFamous title. But since I doubt I'll buy the PS4 until long after launch (if at all), it doesn't matter.

I was really surprised. Also, I think the most understated feature is the ability to immediately return to gameplay when you turn the console off. That's a game changer. I can only hope the Next-box has something similar.

I don't remember them saying anything during the conference, but they made a press release that confirmed it:

Through PS4, users are able to deepen their connections through co-op play or “cross-game chat”.

They also made a press release about the new Dualshock and confirmed bundled headsets, so hopefully online games won't feel so dead.

In addition, DUALSHOCK?4 will come with a built-in speaker and stereo headset jack, enabling PS4 users to enjoy high-fidelity sound effects of games from both the TV and also from the controller. Combined with the Mono Headset that will be bundled with PS4, gamers will also be able to chat with friends playing online, while hearing sound effects from the controller in hand.

As long as the PS4 comes out before Christmas in Europe, I can see myself getting one.

The controller looks really good. It actually looks better than the 360 controller, especially when you consider the dpad which MS still hasn't gotten right. This is the first time a Playstation controller looks comfortable to me.

It's not that Microsoft hasn't gotten the controller right, it's just that they can't make one similar to Sony or Nintendo because of copyrights. The best we'll get to that is with the newer controller that allow you to adjust to the kind of dpad you prefer.
I'm really glad to see they are finally putting headsets with them now. Now if they can really push the Vita with better titles, and hit E3 hard with some amazing game demos then they might very well take the lead this generation. Anyone hear if Microsoft is going to do a conference before E3 for their new console in response to this?

I think we'll get PS1/2 emulation with Sony doing everything possible to get PS3 emulation. It makes sense financially; Sony can make money on the PS store and PS+ subscriptions. Also people can sell in PS3's (and to a less extent, PS2's) to cover the cost of their new PS4. It's win/win if it works.
From what I've read (didn't watch the conference), Sony basically told everyone what they wanted to hear except for the lack of BC and a fixed price, so I was pleasantly surprised. I was even more surprised when Sony announced 8 gigs of DDR5. The small memory pool of the PS360 has been developer's biggest hurdle the last few years, and it's nice to see Sony/MS putting plenty in the machine this time around.
I'm very concerned about the games though. The biggest criticism of the conference is that Sony didn't show us anything new or attention grabbing, with the exception of the hilarious Diablo 3 port. If you can't run Diablo 3 on your computer, you need a new one, not a PS4.

Blizzard is attempting to gain a hold of the console market which is much more significant than what it is on PC. It has nothing to do with having a computer to be able to run the game. With that said, it would have been more exciting with them to do a HD port of Diablo 2 instead.
They are going to stream the previous generation of PS1/2/3 games (like I said in the OP) which makes sense because of with the hardware being completely different. Because of this, I don't see them taking more time to work out emulation.

I know what Blizzard is trying to do, but it just seems silly. Had Diablo 3 launched with the PC version on PS3, I would understand. But they're relaunching a game on Sony's systems 1 1/2 years after the initial release that anyone running Windows 7 could already play. If a person was interested in Diablo 3, they'd be playing it. I don't think a console release is going to push enough sales to justify the cost.

PS1/2 is just a matter of getting an emulator working right. PS1 should be easy. PS2 should be manageable with the new hardware. In fact, the PS3's problems software emulating PS2 games is twofold, and both easily solved on PS4. You can read more details here, but here's the summary.

1) The GPU cannot handle the emulation and cannot call on the CPU for help.
2) The emulator was written by chimpanzees.